Tutor:

New! Get regular updates about newly solved problems via algebra.com's RSS system.

---

Recent problems solved by 'richwmiller'

richwmiller answered: 9132 problems
Jump to solutions: 0..29 , 30..59 , 60..89 , 90..119 , 120..149 , 150..179 , 180..209 , 210..239 , 240..269 , 270..299 , 300..329 , 330..359 , 360..389 , 390..419 , 420..449 , 450..479 , 480..509 , 510..539 , 540..569 , 570..599 , 600..629 , 630..659 , 660..689 , 690..719 , 720..749 , 750..779 , 780..809 , 810..839 , 840..869 , 870..899 , 900..929 , 930..959 , 960..989 , 990..1019 , 1020..1049 , 1050..1079 , 1080..1109 , 1110..1139 , 1140..1169 , 1170..1199 , 1200..1229 , 1230..1259 , 1260..1289 , 1290..1319 , 1320..1349 , 1350..1379 , 1380..1409 , 1410..1439 , 1440..1469 , 1470..1499 , 1500..1529 , 1530..1559 , 1560..1589 , 1590..1619 , 1620..1649 , 1650..1679 , 1680..1709 , 1710..1739 , 1740..1769 , 1770..1799 , 1800..1829 , 1830..1859 , 1860..1889 , 1890..1919 , 1920..1949 , 1950..1979 , 1980..2009 , 2010..2039 , 2040..2069 , 2070..2099 , 2100..2129 , 2130..2159 , 2160..2189 , 2190..2219 , 2220..2249 , 2250..2279 , 2280..2309 , 2310..2339 , 2340..2369 , 2370..2399 , 2400..2429 , 2430..2459 , 2460..2489 , 2490..2519 , 2520..2549 , 2550..2579 , 2580..2609 , 2610..2639 , 2640..2669 , 2670..2699 , 2700..2729 , 2730..2759 , 2760..2789 , 2790..2819 , 2820..2849 , 2850..2879 , 2880..2909 , 2910..2939 , 2940..2969 , 2970..2999 , 3000..3029 , 3030..3059 , 3060..3089 , 3090..3119 , 3120..3149 , 3150..3179 , 3180..3209 , 3210..3239 , 3240..3269 , 3270..3299 , 3300..3329 , 3330..3359 , 3360..3389 , 3390..3419 , 3420..3449 , 3450..3479 , 3480..3509 , 3510..3539 , 3540..3569 , 3570..3599 , 3600..3629 , 3630..3659 , 3660..3689 , 3690..3719 , 3720..3749 , 3750..3779 , 3780..3809 , 3810..3839 , 3840..3869 , 3870..3899 , 3900..3929 , 3930..3959 , 3960..3989 , 3990..4019 , 4020..4049 , 4050..4079 , 4080..4109 , 4110..4139 , 4140..4169 , 4170..4199 , 4200..4229 , 4230..4259 , 4260..4289 , 4290..4319 , 4320..4349 , 4350..4379 , 4380..4409 , 4410..4439 , 4440..4469 , 4470..4499 , 4500..4529 , 4530..4559 , 4560..4589 , 4590..4619 , 4620..4649 , 4650..4679 , 4680..4709 , 4710..4739 , 4740..4769 , 4770..4799 , 4800..4829 , 4830..4859 , 4860..4889 , 4890..4919 , 4920..4949 , 4950..4979 , 4980..5009 , 5010..5039 , 5040..5069 , 5070..5099 , 5100..5129 , 5130..5159 , 5160..5189 , 5190..5219 , 5220..5249 , 5250..5279 , 5280..5309 , 5310..5339 , 5340..5369 , 5370..5399 , 5400..5429 , 5430..5459 , 5460..5489 , 5490..5519 , 5520..5549 , 5550..5579 , 5580..5609 , 5610..5639 , 5640..5669 , 5670..5699 , 5700..5729 , 5730..5759 , 5760..5789 , 5790..5819 , 5820..5849 , 5850..5879 , 5880..5909 , 5910..5939 , 5940..5969 , 5970..5999 , 6000..6029 , 6030..6059 , 6060..6089 , 6090..6119 , 6120..6149 , 6150..6179 , 6180..6209 , 6210..6239 , 6240..6269 , 6270..6299 , 6300..6329 , 6330..6359 , 6360..6389 , 6390..6419 , 6420..6449 , 6450..6479 , 6480..6509 , 6510..6539 , 6540..6569 , 6570..6599 , 6600..6629 , 6630..6659 , 6660..6689 , 6690..6719 , 6720..6749 , 6750..6779 , 6780..6809 , 6810..6839 , 6840..6869 , 6870..6899 , 6900..6929 , 6930..6959 , 6960..6989 , 6990..7019 , 7020..7049 , 7050..7079 , 7080..7109 , 7110..7139 , 7140..7169 , 7170..7199 , 7200..7229 , 7230..7259 , 7260..7289 , 7290..7319 , 7320..7349 , 7350..7379 , 7380..7409 , 7410..7439 , 7440..7469 , 7470..7499 , 7500..7529 , 7530..7559 , 7560..7589 , 7590..7619 , 7620..7649 , 7650..7679 , 7680..7709 , 7710..7739 , 7740..7769 , 7770..7799 , 7800..7829 , 7830..7859 , 7860..7889 , 7890..7919 , 7920..7949 , 7950..7979 , 7980..8009 , 8010..8039 , 8040..8069 , 8070..8099 , 8100..8129 , 8130..8159 , 8160..8189 , 8190..8219 , 8220..8249 , 8250..8279 , 8280..8309 , 8310..8339 , 8340..8369 , 8370..8399 , 8400..8429 , 8430..8459 , 8460..8489 , 8490..8519 , 8520..8549 , 8550..8579 , 8580..8609 , 8610..8639 , 8640..8669 , 8670..8699 , 8700..8729 , 8730..8759 , 8760..8789 , 8790..8819 , 8820..8849 , 8850..8879 , 8880..8909 , 8910..8939 , 8940..8969 , 8970..8999 , 9000..9029 , 9030..9059 , 9060..9089 , 9090..9119 , 9120..9149, >>Next

Rational-functions/283141: I'm getting a little lost on these... 5 - 2 __ n-3 ___________ 4 - 1 __ n-3 I know I need the same on the botton...but can't seem to come up with the right answer...Thanks for your help!!!!! 1 solutions Answer 205555 by richwmiller(9143)   on 2010-03-20 13:14:29 (Show Source): You can put this solution on YOUR website! If the numerator reads 5-(2/(n-3)) and the denominator reads and the whole mess is then multiply the whole shebang by which will get you

logarithm/283139: Hi, I thought I was finally getting the hang of this? I was hit with Find the natural logarithm of the given number, 68.5 I finally understand how to solve equations with the logs, etc.. But I have never just dealt with one number. Is someone able to tell me how i go about this, do I find a way to put in an equation form? Thanks!! Nathalie 1 solutions Answer 205552 by richwmiller(9143)   on 2010-03-20 13:00:52 (Show Source): You can put this solution on YOUR website! natural log(68.5) = 4.22683375

Quadratic_Equations/283119: Bsed on this data, who would you say is a safer driver: a 16 year old, or a 70 year old? Age Accidents per 100 Million miles driven 25 430 30 340 40 220 45 190 55 190 60 220 Explain your answer. Use the quadratic equation and graph to solve. 1 solutions Answer 205549 by richwmiller(9143)   on 2010-03-20 12:51:01 (Show Source): You can put this solution on YOUR website! You don't need anything fancy to tell that the best drivers are around 50 The younger drivers are the worst.

Percentage-and-ratio-word-problems/283132: Patricia has two jobs at the supermarket she works 15 hours every week and makes 120 dollars there every week at the restaurant she works 15 hours a week and get 150 dollars a week in percentage how much more does patricia earn at the restaurant than the supermarket 1 solutions Answer 205547 by richwmiller(9143)   on 2010-03-20 12:44:52 (Show Source): You can put this solution on YOUR website! (150/120)=15/12=(5/4)*100=125% of the supermarket 25% more than the supermarket.

Linear-equations/283134: 1 solutions Answer 205544 by richwmiller(9143)   on 2010-03-20 12:27:57 (Show Source): You can put this solution on YOUR website! Some website rules that you won't like. 1- ONE (1) problem per submission 2- NO similar problems 3- Limit Four(4) submissions daily

Linear-systems/283131: 3x-2y=10, 2x+3y=-2 by substitution 1 solutions Answer 205543 by richwmiller(9143)   on 2010-03-20 12:25:32 (Show Source): You can put this solution on YOUR website! substitution is the harder way to go. This was made for elimination or subtraction/addition 3x-2y=10 2x+3y=-2 First by elimination or addition multiply first by 3 and second by 2 9x-6y=30 4x+6y=-4 add 13x=26 x=2 2x+3y=-2 4+3y=-2 3y=-6 y=-2 (2,-2) now by substitution 3x-2y=10 2x+3y=-2 solve first for x 3x=10+2y x=10/3+2y/3 plug it in the second 2*(10/3+2y/3)+3y=-2 20/3+4y/3+3y=-2 multiply by 3 20+4y+9y=-6 13y=-26 y=-2 plug it in any equation and solve for x 3x-2y=10 3x-2*(-2)=10 3x+4=10 3x=6 x=2

Travel_Word_Problems/283128: Spike averaged 45 mph driving from Rochester to Syracuse and 49 mph driving from Syracuse to Albany. If he drove a total of 237 miles in 5 hours, then how far is it from Syracuse to Albany? 1 solutions Answer 205540 by richwmiller(9143)   on 2010-03-20 12:09:43 (Show Source): You can put this solution on YOUR website! 45x+49y=237 x+y=5 There are several reasons why it is important to put your problem in the correct category. One some tutors only do specific types of problems. For others who actually look up similar problems. This same problem was solved a couple weeks ago.

Quadratic_Equations/283130: Help me solve 4x + x(x-2)=0 1 solutions Answer 205538 by richwmiller(9143)   on 2010-03-20 12:05:00 (Show Source): You can put this solution on YOUR website! some website rules you will not like limit one problem per submission not two not three no similar problems limit 4 submissions daily 4x+x*(x-2)=0 deal with the parentheses first x^2-2x+4x=0 x^2+2x=0 x*(x+2)=0 x=0 x=-2 BTW Your second problem is incomplete. There is no equal sign I am not going to guess where it belongs but it might be identical to the first problem.

Linear_Equations_And_Systems_Word_Problems/283125: Tickets for one show on the Harlem Globetrotters '2006 "Unstoppable" Tour cost $14, $20, or, for VIP seats, $50. So far, five times as many $14 tickets have been sold as VIP tickets. The number of $14 tickets is 15 more than the sum of the number of $20 tickets and the number of VIP tickets. Sales of all three kinds of tickets total $11,700. how many of each kind of ticket have been sold? 1 solutions Answer 205537 by richwmiller(9143)   on 2010-03-20 11:56:41 (Show Source): You can put this solution on YOUR website! v=vip $50 m= middle price $20 r=regular admission $14 50v+20m+14r=11700 5v=r r=15+m+v m = 225, r = 300, v = 60

Mixture_Word_Problems/283127: A farmer wants to mix a liquid fertilizer that contains 2% nitrogen with one that contains 10% nitrogen to obtain 40 gallons of a fertilizer that contains 8% nitrogen. How many gallons of each fertilizer should be used? 1 solutions Answer 205536 by richwmiller(9143)   on 2010-03-20 11:51:06 (Show Source): You can put this solution on YOUR website! .02x+.10y=40*.08 x+y=40 x=10 y=30

Linear_Equations_And_Systems_Word_Problems/283124: I am having a problem with this problem. Can you please help me? The perimeter of a triangle is 70cm. The longest side is 4cm less than the sum of the other two sides. Twice the shortest side is 9cm less than the longest side. Find the length of each side of the triangle. 1 solutions Answer 205535 by richwmiller(9143)   on 2010-03-20 11:48:37 (Show Source): You can put this solution on YOUR website! We have three unknowns (a,b,c ) so we need three equations. a+b+c=70 perimeter is 70 c=a+b-4 longest side c is 4cm less than the sum of the other two sides a+b c=2a-9 twice the shortest side a is 9 cm less than the longest side c a+b+c=70 c=a+b-4 c=2a-9 I leave the details to you. a = 12, b = 25, c = 33 Any problems let me know.

test/283120: make x the subjects of: x+y=w 1 solutions Answer 205533 by richwmiller(9143)   on 2010-03-20 11:27:57 (Show Source): You can put this solution on YOUR website! Some website rules that you won't like. one problem per submission no similar problems limit 4 problems daily. x+y=w To make x the subject you want to add , subtract multiply or divide to get x to be the only thing on its side.

Geometry_Word_Problems/283118: A 10-foot ladder reaches a height of 8 feet when placed against the side of a building. How far from the base of the building is the ladder? 1 solutions Answer 205532 by richwmiller(9143)   on 2010-03-20 11:24:20 (Show Source): You can put this solution on YOUR website! The hypotenuse is 10 one of the sides is 8. This is a multiple of the 3,4,5 triangle so it is 6 feet from the base. you can verify that with a^2+8^2=10^

Linear-equations/283039: . Simplify - 5 (7 – 2 ) – 3(4 – 7 ) 1 solutions Answer 205516 by richwmiller(9143)   on 2010-03-20 09:06:32 (Show Source): You can put this solution on YOUR website! deal with parentheses first -5*7-5*(-2)-3*(4)-3*(-7) -35+10-12+21 rearrange(not necessary) 10+21-35-12 31-47= -16 one problem per submission and no similar problems are two of the website rules

percentage/283092: You have 63 clients to interview and you only finished 28. Round answer to nearest tenth and tell how much percentage have been finished. I need to see the problem worked out. Thank you. 1 solutions Answer 205515 by richwmiller(9143)   on 2010-03-20 09:01:00 (Show Source): You can put this solution on YOUR website! 28*100/63=7*4*100/7*9= i leave the rest for you to enjoy.

Coordinate-system/283059: |9x - 2| = |8x - 5| 1 solutions Answer 205514 by richwmiller(9143)   on 2010-03-20 08:57:59 (Show Source): You can put this solution on YOUR website! |9x - 2| = |8x - 5| 9x-2=8x-5 x=-3 |9x - 2| = |-(8x - 5)| 9x-2=-8x+5 17x=7 x=7/17 |-(9x - 2)| = |8x - 5| -9x+2=8x-5 7=17x 7/17=x |-(9x - 2)| = |-(8x - 5)| -9x+2=-8x+5 -3=x so we have two distinct answers x=-3 and x=7/17

Linear-equations/283041: Please help me? Use the slope-intercept form. Find the equation of the line that contains the point (-3, 4) and has slope -3/4. 1 solutions Answer 205513 by richwmiller(9143)   on 2010-03-20 08:36:34 (Show Source): You can put this solution on YOUR website! So what is the slope intercept form? plug in the values given and find b then re write the slope intercept form with the slope and the new found b

Inequalities/283084: Given | 2x – 7 | > 7. Solve for x. a) x < -7 or x > 7 b) x < -7/2 or x > 7/2 c) x < 0 or x > 7 d) x < -2/7 or x > 7 1 solutions Answer 205512 by richwmiller(9143)   on 2010-03-20 08:34:24 (Show Source): You can put this solution on YOUR website! 2x-7>7 2x>14 x>7 and 7-2x>7 -2x>0 divide by -2 and change sign x<0 answer c)x<0 or x>7

Linear-equations/283091: How do I do the following 2 problems related to parallels and perpendiculars? "Write an equation of the line through the point (a) parallel to the given line and (b) perpendicular to the given line". I must show my work. I am a 53 year old non-traditional student, and this algebra is really difficult for me to understand. Thank you so much for your time, I really appreciate it! Have a blessed day...Kathye Watson 1. Point = (3, -2) Line = 5x - 4y = 8 a)parallel = ? b)perpendicular = ? 1 solutions Answer 205510 by richwmiller(9143)   on 2010-03-20 08:30:01 (Show Source): You can put this solution on YOUR website! parallel has the same slope m perpendicular slope m/-1 1-slope = -a/b -5/-4=5/4 parallel 5/4 3,-2 y=5/4x+b -2=5/4*3+b -8/4-15/4=b -23/4=b y=5x/4-23/4 or 4y=5x-23 perp -4/5 y=-4/5+b -2=-4/5*3+b -10/5+12/5=b 2/5=b y=-4/5x+2/5 or 5y=-4x+2 or 4x+5y=2 Now you get to try it on 2. Point = (-8, 3) Line = 2x + 3y = 5 a)parallel = ? b)perpendicular = ? first get the slope -a/b a=2 b=3 NB this b is not the same as the b of y=mx+b this b comes from ax+by+c=0

Angles/283046: Three angles of a quadrilateral each measure 87 degrees. What is the measure of the fourth angle? 1 solutions Answer 205509 by richwmiller(9143)   on 2010-03-20 08:19:22 (Show Source): You can put this solution on YOUR website! 360-3*87

Rectangles/283090: The length of this rectangle is 1cm more than its width.It has an area of 232cm2.Find the width of the rectangle correct to 1 d.p. 1 solutions Answer 205508 by richwmiller(9143)   on 2010-03-20 08:17:37 (Show Source): You can put this solution on YOUR website! x*(x+1)=232 x^2+x-232=0 we only use the positive root 14.7 for the width length would be 14.7+1 Solved by pluggable solver: SOLVE quadratic equation with variable Quadratic equation (in our case ) has the following solutons: For these solutions to exist, the discriminant should not be a negative number. First, we need to compute the discriminant : . Discriminant d=929 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 14.7397506541282, -15.7397506541282. Here's your graph:

Average/283086: Janine received test scores of 88%, 92%, 79%, 94%, and 86%. What is the minimum score she must receive on her final exam if the five test scores are weighted equally, the final exam score is weighted twice as much as each test score, and if she wishes to have an overall average of 91%? a) 91% b) 95% c) 89% d) 99% e) It is impossible for her to score high enough on the final exam to have an overall average of 91%. 1 solutions Answer 205507 by richwmiller(9143)   on 2010-03-20 08:08:02 (Show Source): You can put this solution on YOUR website! (88+92+79+94+86+2x)/7=91 Answer x=99 If she gets 95.5 she can get a 90% average which is still an A in many schools.

Miscellaneous_Word_Problems/283087: What is the degree measure of the smaller angle formed by the hands of a clock at 10 o'clock?? a) 30 b) 45 c) 60 d) 75 e) 90 1 solutions Answer 205506 by richwmiller(9143)   on 2010-03-20 07:59:43 (Show Source): You can put this solution on YOUR website! At ten o'clock the hands form an angle 2/12*360=60 degrees

Rate-of-work-word-problems/283085: Pipes A, B, and C individually drain a basin in 3, 2, and 1.5 hours respectively. If they were all opened to drain the basin together, how many minutes would it take? a) 20 b) 40 c) 60 d) 90 1 solutions Answer 205505 by richwmiller(9143)   on 2010-03-20 07:56:23 (Show Source): You can put this solution on YOUR website! x/3+x/2+x/1.5=1 multiply by 6 2x+3x+4x=6 9x=6 x=6/9=2/3 hour 2/3*60=40 minutes b)40

Geometry_Word_Problems/283088: A rectangular garden 50 feet long and 10 feet wide is enclosed by a fence. To make the garden larger, while using the same fence, its shape is changed to a square. By how many square feet does this enlarge the garden? a) 100 b) 200 c) 300 d) 400 e) 500 1 solutions Answer 205504 by richwmiller(9143)   on 2010-03-20 07:52:54 (Show Source): You can put this solution on YOUR website! 50+50+10+10=120 feet of fence 120=4s 30=s 30^2=900 50*10=500 900-500=400 d)400

absolute-value/283073: How many solutions are there for the equation x + 2 = | x – 3 | ? a) 0 b) 1 c) 2 d) 3 e) none of these 1 solutions Answer 205502 by richwmiller(9143)   on 2010-03-20 07:34:12 (Show Source): You can put this solution on YOUR website! x+2=|x-3| has only one solution x+2=-(x-3) x+2=-x+3 2x=1 x=1/2 ok and x+2=+(x-3) x+2=x-3 0=-5 not a solution so there is only one solution

Polynomials-and-rational-expressions/283078: The sum of the solutions of the equation x^4 + 2x^3 − 13x^2 − 14x + 24 = 0 Is (A) −2 (B) −1 (C) 0 (D) 1 (E) 2 1 solutions Answer 205497 by richwmiller(9143)   on 2010-03-20 07:15:40 (Show Source): You can put this solution on YOUR website! (x-3) (x-1) (x+2) (x+4) = 0 3+1-2-4=-2 Answer: (A)-2

Square-cubic-other-roots/283062: Hi, how would you simplify the following algebraic expression? 1 solutions Answer 205496 by richwmiller(9143)   on 2010-03-20 07:12:29 (Show Source): You can put this solution on YOUR website! Answer: n^4/m*r^4 since m^2/m^3=1/m and n^3/n^(-1)=n^4 and r^(-3)/r=1/r^4

Average/283079: The average (arithmetic mean) age of a group consisting of teachers and engineers is 40. If the teachers average 35 and the engineers 50 years old, then the ratio of the number of teachers to the number of engineers is: (A) 3 : 2 (B) 3 : 1 (C) 2 : 3 (D) 2 : 1 (E) 1 : 2 1 solutions Answer 205492 by richwmiller(9143)   on 2010-03-20 07:03:08 (Show Source): You can put this solution on YOUR website! 35t+50e/(t+e)=40 35t+50e=40*(t+e) 35t+50e=40t+40e 10e=5t 10/5=t/e 2/1=t/e (D) 2:1

Geometry_Word_Problems/283082: Four pennies of diameter d are placed with their centers on the four corners of a d x d square. the percentage of the area of the square covered by the pennies is A 60 to 70 b 70 to 80 c 80 to 90 d 90 to 100 e none of these 1 solutions Answer 205491 by richwmiller(9143)   on 2010-03-20 06:57:18 (Show Source): You can put this solution on YOUR website! we have 4*1/4 =1 penny area of a penny pi*(d/2)^2=3.14*d^2/4=3.14/4*d^2 area of the square is d^2 3.14/4 *100 is the percentage of the square covered by the pennies 3.14/4 *100=78.5 so b) 70-80

Square-cubic-other-roots/283064: I am having a lot of trouble with this question 1 solutions Answer 205490 by richwmiller(9143)   on 2010-03-20 06:50:42 (Show Source): You can put this solution on YOUR website! There is no question. That is an expression. Do you want to ask a question about the expression? I didn't think so. It could be combined to form one fraction 1/(x-y) y/(x^2-xy) + 1/x factor y/(x*(x-y))+1/x y/x*(x-y)+(x-y)/(x*(x-y)) y+x-y/(x*(x-y) x/x*(x-y) 1/(x-y)